Despite the profound sense of sadness that has fallen over South Africa with the passing of their former president Nelson Mandela, mourners said it was also a time to celebrate the achievements of the anti-apartheid leader who emerged from prison to become South Africa's first black president.

Mandela's body was moved early this morning from Johannesburg to Pretoria's One Military Hospital. Mandela's coffin was draped in South Africa's flag. The black SUV-type vehicle containing Mandela's coffin was escorted by the military.

There will now be 10 days of national mourning throughout the country. A memorial service will be held Dec. 10 at a stadium in Johannesburg. His body will lie in state in Pretoria from Dec. 11-13 so that South Africans can pay their final respects. He will then be taken to his ancestral village of Qunu on Dec.15 where he'll be buried alongside three of his children who are deceased.

Meanwhile, Nelson Mandela's eldest grandson said his family has been overwhelmed by the global outpouring of support since the passing of the 95-year-old former president.

Retired Archbishop Desmond Tutu remembered Mandela, saying, "What's going to happen to us now that our father has died..The sun will rise tomorrow, the next day and the next. It won't be as bright as yesterday but it will carry on."

The people of South Africa reacted with deep sadness at the loss of a man considered by many to be the father of the nation. But the somber scenes outside Mandela's home in the Johannesburg suburb of Houghton were replaced today with throngs of people singing old songs of struggle from the apartheid era and the country's national anthem.

"You know, it's tragic, it's sad. But at the same time, I think we should celebrate," Mandela supporter Hamsa Moosa told ABC News. "Celebrate what he has achieved and what he's given us. I wouldn't be here, I wouldn't be free if it wasn't for him."

A man blew on a vuvuzela, the plastic horn widely used at World Cup soccer games in South Africa in 2010, which was the site of Mandela's final public appearance. Others shouted "Nelson!" and Viva Madiba!" -- referring to Mandela by his clan name.

A makeshift shrine of candles, a national flag and bouquets of flowers has begun to grow precipitously. A framed portrait of a smiling Mandela was propped against a tree with the caption: "Rest in peace, Madiba." Mandela had been receiving medical care in the home in past months, where he had been in "serious but stable condition" because of a chronic lung infection.

Mandela's oldest grandson, Mandla Mandela (also known by his full name Nkosi Zwelivelile Mandela) said he is "deeply saddened," but is "strengthened by the knowledge that he is now finally resting."

"All that I can do is thank God that I had a grandfather who loved and guided all of us in the family. The best lesson that he taught all of us was the need for us to be prepared to be of service to our people," Mandla said in a statement, the first public comment from anti-apartheid leader's family since his death.

Mandla said his grandfather "demonstrated his fighting spirit" during his most recent health battles.

"He is an embodiment of strength, struggle and survival, principles that are cherished by humanity. As a grandfather, we have all known him as a kind hearted, generous and wise person who was always prepared to offer us advice on how to be good members of our communities," Mandla said.

"Celebrating his long life is the best accolade we can give him. Celebrating his contribution to society will make him smile in his resting place. We look forward to continue our interaction with him as one of our beloved ancestor," the statement concluded.

Celebrations of Mandela's life also took place near a home in Soweto, South Africa, where the global icon once lived. These scenes swept across the country, growing into the wee hours of the morning after South African president Jacob Zuma broke the news to the nation and the world Thursday night.

"He is now resting. He is now at peace. Our nation has lost its greatest son. Our people have lost a father," Zuma said.

Mourners Outside Mandela's House Celebrate His Life

Some people flocked to Mandela's home still wearing their pajamas. Many who showed up to pay their respects were understandably overcome with grief.

"I'm disappointed. I'm said," Mandela supporter Thumelo Madikwe told ABC News. "But at the same time, I think he's had his part in life and he did it very well. It's fine that he goes. He did all he could."

Mandela's youngest daughters, Zindzi and Zenani, were attending the Royal Premiere of the new biopic, "Mandela: Long Walk to Freedom," when they learned of his death.

"They received the news of their father's passing during the screening and immediately left the cinema," the Nelson Mandela Foundation said in a statement.

After the Mandela photo montage played over the credits, the house lights came up at the Odeon Leicester Square theater and an announcement was made and a moment of silence was observed by the cast, including the film's star Idris Elba, who played Mandela.

The Duke and Duchess of Cambridge were also on hand for the premiere and apparently learned of Mandela's death while the movie was in progress. They left after the credits.

Mandela was surrounded by family when he passed away Thursday.

ABC News' and Alexander Marquardt and The Associated Press contributed to this report.